0.1 \(\lesssim x \lesssim 1, \qquad y < 1.\)

] Excitations in this region consist of nonlinear coherent wave packets produced by mode coupling. Although they remain below the persistence threshold, these structures serve as the intermediate states that generate the first persistent excitations of the CTS hierarchy.

Closure Survival This section examines the first region above the persistence threshold, where geometric closure produces stable vortex-ring structures.